Homemade cinnamon rolls with maple cream cheese

For the Dough:
1 cup warm milk (105-110 degrees)
2 1/2 teaspoons instant dry yeast
2 eggs at room temperature
1/3 cup salted butter (barley melted but not super hot)
4 1/2 cups all-purpose flour (divided)
1 teaspoon salt
1/2 cup granulated sugar
For the Filling:
3/4 cup salted butter (almost melted)
1 cup packed brown sugar
2 tablespoons cinnamon
1/2 cup heavy cream*** (for pouring over the risen rolls)
For the Frosting:
6 ounces cream cheese (softened)
1/3 cup salted butter (softened)
2 cups powdered sugar
1/2 tablespoon maple extract (or vanilla)